Random matrix theory improved Fréchet mean of symmetric positive definite matrices

Florent Bouchard, Ammar Mian, Malik Tiomoko, Guillaume Ginolhac, Frederic Pascal
Proceedings of the 41st International Conference on Machine Learning, PMLR 235:4403-4415, 2024.

Abstract

In this study, we consider the realm of covariance matrices in machine learning, particularly focusing on computing Fréchet means on the manifold of symmetric positive definite matrices, commonly referred to as Karcher or geometric means. Such means are leveraged in numerous machine learning tasks. Relying on advanced statistical tools, we introduce a random matrix theory based method that estimates Fréchet means, which is particularly beneficial when dealing with low sample support and a high number of matrices to average. Our experimental evaluation, involving both synthetic and real-world EEG and hyperspectral datasets, shows that we largely outperform state-of-the-art methods.

Cite this Paper

BibTeX
@InProceedings{pmlr-v235-bouchard24a, title = {Random matrix theory improved Fréchet mean of symmetric positive definite matrices}, author = {Bouchard, Florent and Mian, Ammar and Tiomoko, Malik and Ginolhac, Guillaume and Pascal, Frederic}, booktitle = {Proceedings of the 41st International Conference on Machine Learning}, pages = {4403--4415}, year = {2024}, editor = {Salakhutdinov, Ruslan and Kolter, Zico and Heller, Katherine and Weller, Adrian and Oliver, Nuria and Scarlett, Jonathan and Berkenkamp, Felix}, volume = {235}, series = {Proceedings of Machine Learning Research}, month = {21--27 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v235/main/assets/bouchard24a/bouchard24a.pdf}, url = {https://proceedings.mlr.press/v235/bouchard24a.html}, abstract = {In this study, we consider the realm of covariance matrices in machine learning, particularly focusing on computing Fréchet means on the manifold of symmetric positive definite matrices, commonly referred to as Karcher or geometric means. Such means are leveraged in numerous machine learning tasks. Relying on advanced statistical tools, we introduce a random matrix theory based method that estimates Fréchet means, which is particularly beneficial when dealing with low sample support and a high number of matrices to average. Our experimental evaluation, involving both synthetic and real-world EEG and hyperspectral datasets, shows that we largely outperform state-of-the-art methods.} }
Endnote
%0 Conference Paper %T Random matrix theory improved Fréchet mean of symmetric positive definite matrices %A Florent Bouchard %A Ammar Mian %A Malik Tiomoko %A Guillaume Ginolhac %A Frederic Pascal %B Proceedings of the 41st International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2024 %E Ruslan Salakhutdinov %E Zico Kolter %E Katherine Heller %E Adrian Weller %E Nuria Oliver %E Jonathan Scarlett %E Felix Berkenkamp %F pmlr-v235-bouchard24a %I PMLR %P 4403--4415 %U https://proceedings.mlr.press/v235/bouchard24a.html %V 235 %X In this study, we consider the realm of covariance matrices in machine learning, particularly focusing on computing Fréchet means on the manifold of symmetric positive definite matrices, commonly referred to as Karcher or geometric means. Such means are leveraged in numerous machine learning tasks. Relying on advanced statistical tools, we introduce a random matrix theory based method that estimates Fréchet means, which is particularly beneficial when dealing with low sample support and a high number of matrices to average. Our experimental evaluation, involving both synthetic and real-world EEG and hyperspectral datasets, shows that we largely outperform state-of-the-art methods.
APA
Bouchard, F., Mian, A., Tiomoko, M., Ginolhac, G. & Pascal, F.. (2024). Random matrix theory improved Fréchet mean of symmetric positive definite matrices. Proceedings of the 41st International Conference on Machine Learning, in Proceedings of Machine Learning Research 235:4403-4415 Available from https://proceedings.mlr.press/v235/bouchard24a.html.

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